B-258 SOLUTIONS
CHAPTER 17
FINANCIAL LEVERAGE AND CAPITAL
STRUCTURE POLICY
Answers to Concepts Review and Critical Thinking Questions
1. Business risk is the equity risk arising from the nature of the firm’s operating activity, and is directly
related to the systematic risk of the firm’s assets. Financial risk is the equity risk that is due entirely
to the firm’s chosen capital structure. As financial leverage, or the use of debt financing, increases,
so does financial risk and, hence, the overall risk of the equity. Thus, Firm B could have a higher
cost of equity if it uses greater leverage.
2.
No, it doesn’t follow. While it is true that the equity and debt costs are rising, the key thing to
remember is that the cost of debt is still less than the cost of equity. Since we are using more and
more debt, the WACC does not necessarily rise.
3. Because many relevant factors such as bankruptcy costs, tax asymmetries, and agency costs cannot
easily be identified or quantified, it’s practically impossible to determine the precise debt/equity ratio
that maximizes the value of the firm. However, if the firm’s cost of new debt suddenly becomes
much more expensive, it’s probably true that the firm is too highly leveraged.
4.
The more capital intensive industries, such as airlines, cable television, and electric utilities, tend to
use greater financial leverage. Also, industries with less predictable future earnings, such as
computers or drugs, tend to use less financial leverage. Such industries also have a higher
concentration of growth and startup firms. Overall, the general tendency is for firms with
identifiable, tangible assets and relatively more predictable future earnings to use more debt
financing. These are typically the firms with the greatest need for external financing and the greatest
likelihood of benefiting from the interest tax shelter.
5.
It’s called leverage (or “gearing” in the UK) because it magnifies gains or losses.
6.
Homemade leverage refers to the use of borrowing on the personal level as opposed to the corporate
level.
7.
One answer is that the right to file for bankruptcy is a valuable asset, and the financial manager acts
in shareholders’ best interest by managing this asset in ways that maximize its value. To the extent
that a bankruptcy filing prevents “a race to the courthouse steps,” it would seem to be a reasonable
use of the process.
8.
As in the previous question, it could be argued that using bankruptcy laws as a sword may simply be
the best use of the asset. Creditors are aware at the time a loan is made of the possibility of
bankruptcy, and the interest charged incorporates it.
CHAPTER 17 B-259
9.
One side is that Continental was going to go bankrupt because its costs made it uncompetitive. The
bankruptcy filing enabled Continental to restructure and keep flying. The other side is that
Continental abused the bankruptcy code. Rather than renegotiate labor agreements, Continental
simply abrogated them to the detriment of its employees. In this, and the last several, questions, an
important thing to keep in mind is that the bankruptcy code is a creation of law, not economics. A
strong argument can always be made that making the best use of the bankruptcy code is no different
from, for example, minimizing taxes by making best use of the tax code. Indeed, a strong case can be
made that it is the financial manager’s duty to do so. As the case of Continental illustrates, the code
can be changed if socially undesirable outcomes are a problem.
10. The basic goal is to minimize the value of non-marketed claims.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Basic
1.
a.
A table outlining the income statement for the three possible states of the economy is shown
below. The EPS is the net income divided by the 2,500 shares outstanding. The last row shows
the percentage change in EPS the company will experience in a recession or an expansion
economy.
EBIT
Interest
NI
EPS
%EPS
b.
Recession
€6,000
0
€6,000
€ 2.40
–60
Normal
€15,000
0
€15,000
€ 6.00
–––
Expansion
€19,500
0
€19,500
€ 7.80
+30
If the company undergoes the proposed recapitalization, it will repurchase:
Share price = Equity / Shares outstanding
Share price = €150,000/2,500
Share price = €60
Shares repurchased = Debt issued / Share price
Shares repurchased =€60,000/€60
Shares repurchased = 1,000
B-260 SOLUTIONS
The interest payment each year under all three scenarios will be:
Interest payment = €60,000(.05) = €3,000
The last row shows the percentage change in EPS the company will experience in a recession
or an expansion economy under the proposed recapitalization.
EBIT
Interest
NI
EPS
%EPS
2.
a.
Normal
€15,000
3,000
€12,000
€ 8.00
–––
Expansion
€19,500
3,000
€16,500
€11.00
+37.50
A table outlining the income statement with taxes for the three possible states of the economy is
shown below. The share price is still €60, and there are still 2,500 shares outstanding. The last
row shows the percentage change in EPS the company will experience in a recession or an
expansion economy.
EBIT
Interest
Taxes
NI
EPS
%EPS
b.
Recession
€6,000
3,000
€3,000
€2.00
–75.00
Recession
€6,000
0
2,100
€3,900
€1.56
–60
Normal
€15,000
0
5,250
€9,750
€3.90
–––
Expansion
€19,500
0
6,825
€12,675
€5.07
+30
A table outlining the income statement with taxes for the three possible states of the economy
and assuming the company undertakes the proposed capitalization is shown below. The interest
payment and shares repurchased are the same as in part b of Problem 1.
EBIT
Interest
Taxes
NI
EPS
%EPS
Recession
€6,000
3,000
1,050
€1,950
€1.30
–75.00
Normal
€15,000
3,000
4,200
€7,800
€5.20
–––
Expansion
€19,500
3,000
5,775
€10,725
€7.15
+37.50
Notice that the percentage change in EPS is the same both with and without taxes.
CHAPTER 17 B-261
3.
a.
Since the company has a market-to-book ratio of 1.0, the total equity of the firm is equal to the
market value of equity. Using the equation for ROE:
ROE = NI/€150,000
The ROE for each state of the economy under the current capital structure and no taxes is:
ROE
%ROE
Recession
.04
–60
Normal
.10
–––
Expansion
.13
+30
The second row shows the percentage change in ROE from the normal economy.
b.
If the company undertakes the proposed recapitalization, the new equity value will be:
Equity = €150,000 – 60,000
Equity = €90,000
So, the ROE for each state of the economy is:
ROE = NI/€90,000
ROE
%ROE
c.
Recession
.0333
–75.00
Normal
.1333
–––
Expansion
.1833
+37.50
If there are corporate taxes and the company maintains its current capital structure, the ROE is:
ROE
%ROE
.0260
–60
.0650
–––
.0845
+30
If the company undertakes the proposed recapitalization, and there are corporate taxes, the ROE
for each state of the economy is:
ROE
%ROE
.0217
–75.00
.0867
–––
.1192
+37.50
Notice that the percentage change in ROE is the same as the percentage change in EPS. The
percentage change in ROE is also the same with or without taxes.
4.
a.
Under Plan I, the unlevered company, net income is the same as EBIT with no corporate tax.
The EPS under this capitalization will be:
EPS = CNY2,000,000/150,000 shares
EPS = CNY13.33
B-262 SOLUTIONS
Under Plan II, the levered company, EBIT will be reduced by the interest payment. The interest
payment is the amount of debt times the interest rate, so:
NI = CNY2,000,000 – .10(CNY15,000,000)
NI = CNY500,000
And the EPS will be:
EPS = CNY500,000/60,000 shares
EPS = CNY8.33
Plan I has the higher EPS when EBIT is CNY2,000,000.
b.
Under Plan I, the net income is CNY7,000,000 and the EPS is:
EPS = CNY7,000,000/150,000 shares
EPS = CNY46.67
Under Plan II, the net income is:
NI = CNY7,000,000 – .10(CNY15,000,000)
NI = CNY5,500,000
And the EPS is:
EPS = CNY5,500,000/60,000 shares
EPS = CNY91.67
Plan II has the higher EPS when EBIT is CNY7,000,000.
c.
To find the breakeven EBIT for two different capital structures, we simply set the equations for
EPS equal to each other and solve for EBIT. The breakeven EBIT is:
EBIT/150,000 = [EBIT – .10(CNY15,000,000)]/60,000
EBIT = CNY2,500,000
5.
We can find the price per share by dividing the amount of debt used to repurchase shares by the
number of shares repurchased. Doing so, we find the share price is:
Share price = CNY15,000,000/(150,000 – 60,000)
Share price = CNY166.67 per share
The value of the company under the all-equity plan is:
V = CNY166.67(150,000 shares) = CNY2,500,500
And the value of the company under the levered plan is:
V = CNY166.67(60,000 shares) + CNY15,000,000 debt = CNY2,500,200
CHAPTER 17 B-263
6.
a. The income statement for each capitalization plan is:
EBIT
Interest
NI
EPS
I
INR10,000,000
1,700,000
INR8,300,000
II
INR10,000,000
2,800,000
INR7,200,000
All-Equity
INR10,000,000
INR10,000,000
INR7,545.45
INR8,000.00
INR7,142.86
Plan II has the highest EPS; the all-equity plan has the lowest EPS.
b.
The breakeven level of EBIT occurs when the capitalization plans result in the same EPS. The
EPS is calculated as:
EPS = (EBIT – RDD)/Shares outstanding
This equation calculates the interest payment (RDD) and subtracts it from the EBIT, which
results in the net income. Dividing by the shares outstanding gives us the EPS. For the allequity capital structure, the interest term is zero. To find the breakeven EBIT for two different
capital structures, we simply set the equations equal to each other and solve for EBIT. The
breakeven EBIT between the all-equity capital structure and Plan I is:
EBIT/1,400 = [EBIT – .10(INR17,000,00)]/1,100
EBIT = INR7,933,333
And the breakeven EBIT between the all-equity capital structure and Plan II is:
EBIT/1,400 = [EBIT – .10(INR28,000,000)]/900
EBIT = INR7,840,000
The break-even levels of EBIT are the same because of M&M Proposition I.
c.
Setting the equations for EPS from Plan I and Plan II equal to each other and solving for EBIT,
we get:
[EBIT – .10(INR17,000,000)]/1,100 = [EBIT – .10(INR28,000,000)]/900
EBIT = INR7,750,000
This break-even level of EBIT is the same as in part b again because of M&M Proposition I.
B-264 SOLUTIONS
d.
The income statement for each capitalization plan with corporate income taxes is:
I
EBIT
Interest
Taxes
INR10,000,000
1,700,000
3,320,000
NI
II
All-equity
INR10,000,000 INR10,000,000
2,800,000
2,880,000
4,000,000
INR4,980,000
INR4,320,000
INR6,000,000
INR 4,527
INR4,800
INR4,286
EPS
Plan II still has the highest EPS; the all-equity plan still has the lowest EPS.
We can calculate the EPS as:
EPS = [(EBIT – RDD)(1 – tC)]/Shares outstanding
This is similar to the equation we used before, except now we need to account for taxes. Again,
the interest expense term is zero in the all-equity capital structure. So, the breakeven EBIT
between the all-equity plan and Plan I is:
EBIT(1 – .40)/1,400 = [EBIT – .10(INR17,000,000)](1 – .40)/1,100
EBIT = INR7,933,333
The breakeven EBIT between the all-equity plan and Plan II is:
EBIT(1 – .40)/1,400 = [EBIT – .10(INR28,000,000)](1 – .40)/900
EBIT = INR7,840,000
And the breakeven between Plan I and Plan II is:
[EBIT – .10(INR17,000,000)](1 – .40)/1,100 = [EBIT – .10(INR28,000,000)](1 – .40)/900
EBIT = INR7,750,000
The break-even levels of EBIT do not change because the addition of taxes reduces the income
of all three plans by the same percentage; therefore, they do not change relative to one another.
7.
To find the value per share of the stock under each capitalization plan, we can calculate the price as
the value of shares repurchased divided by the number of shares repurchased. So, under Plan I, the
value per share is:
P = INR11,000,000/200 shares
P = INR55,000 per share
And under Plan II, the value per share is:
P = INR28,000,000/500 shares
P = INR56,000 per share
CHAPTER 17 B-265
This shows that when there are no corporate taxes, the stockholder does not care about the capital
structure decision of the firm. This is M&M Proposition I without taxes.
8.
a. The earnings per share are:
EPS = €16,000/2,000 shares
EPS = €8.00
So, the cash flow for the company is:
Cash flow = €8.00(100 shares)
Cash flow = €800
b.
To determine the cash flow to the shareholder, we need to determine the EPS of the firm under
the proposed capital structure. The market value of the firm is:
V = €70(2,000)
V = €140,000
Under the proposed capital structure, the firm will raise new debt in the amount of:
D = 0.40(€140,000)
D = €56,000
in debt. This means the number of shares repurchased will be:
Shares repurchased = €56,000/€70
Shares repurchased = 800
Under the new capital structure, the company will have to make an interest payment on the new
debt. The net income with the interest payment will be:
NI = €16,000 – .10(€56,000)
NI = €10,400
This means the EPS under the new capital structure will be:
EPS = €10,400/1,200 shares
EPS = €8.67
Since all earnings are paid as dividends, the shareholder will receive:
Shareholder cash flow = €8.67(100 shares)
Shareholder cash flow = €866.67
c.
To replicate the proposed capital structure, the shareholder should sell 40 percent of their
shares, or 40 shares, and lend the proceeds at 8 percent. The shareholder will have an interest
cash flow of:
Interest cash flow = 40(€70)(.10)
B-266 SOLUTIONS
Interest cash flow = €280
The shareholder will receive dividend payments on the remaining 60 shares, so the dividends
received will be:
Dividends received = €8.67(60 shares)
Dividends received = €520
The total cash flow for the shareholder under these assumptions will be:
Total cash flow = €280 + 520
Total cash flow = €800
This is the same cash flow we calculated in part a.
9.
d.
The capital structure is irrelevant because shareholders can create their own leverage or unlever
the stock to create the payoff they desire, regardless of the capital structure the firm actually
chooses.
a.
The rate of return earned will be the dividend yield. The company has debt, so it must make an
interest payment. The net income for the company is:
NI = $75,000 – .09($400,000)
NI = $39,000
The investor will receive dividends in proportion to the percentage of the company’s share they
own. The total dividends received by the shareholder will be:
Dividends received = $39,000($30,000/$400,000)
Dividends received = $2,925
So the return the shareholder expects is:
R = $2,925/$30,000
R = .0975 or 9.75%
b.
To generate exactly the same cash flows in the other company, the shareholder needs to match
the capital structure of ABC. The shareholder should sell all shares in XYZ. This will net
$30,000. The shareholder should then borrow $30,000. This will create an interest cash flow
of:
Interest cash flow = .09($30,000)
Interest cash flow = –$2,700
The investor should then use the proceeds of the stock sale and the loan to buy shares in ABC.
The investor will receive dividends in proportion to the percentage of the company’s share they
own. The total dividends received by the shareholder will be:
Dividends received = $75,000($60,000/$600,000)
Dividends received = $7,500
CHAPTER 17 B-267
The total cash flow for the shareholder will be:
Total cash flow = $7,300 – 2,700
Total cash flow = $4,800
The shareholders return in this case will be:
R = $4,800/$30,000
R = .1600 or 16.00%
c.
ABC is an all equity company, so:
RE = RA = $75,000/$600,000
RE = .1250 or 12.50%
To find the cost of equity for XYZ we need to use M&M Proposition II, so:
RE = RA + (RA – RD)(D/E)(1 – tC)
RE = .1250 + (.1250 – .09)(1)(1)
RE = .1600 or 16.00%
d.
To find the WACC for each company we need to use the WACC equation:
WACC = (E/V)RE + (D/V)RD(1 – tC)
So, for ABC, the WACC is:
WACC = (1)(.1250) + (0)(.09)
WACC = .1250 or 12.50%
And for XYZ, the WACC is:
WACC = (1/2)(.16) + (1/2)(.09)
WACC = .1250 or 12.50%
When there are no corporate taxes, the cost of capital for the firm is unaffected by the capital
structure; this is M&M Proposition I without taxes.
10. With no taxes, the value of an unlevered firm is the interest rate divided by the unlevered cost of
equity, so:
V = EBIT/WACC
$40,000,000 = EBIT/.14
EBIT = .14($40,000,000)
EBIT = $5,650,000
B-268 SOLUTIONS
11. If there are corporate taxes, the value of an unlevered firm is:
VU = EBIT(1 – tC)/RU
Using this relationship, we can find EBIT as:
$40,000,000 = EBIT(1 – .35)/.14
EBIT = $8,615,684.62
The WACC remains at 14 percent. Due to taxes, EBIT for an all-equity firm would have to be
higher for the firm to still be worth $40 million.
12. a.
With the information provided, we can use the equation for calculating WACC to find the cost
of equity. The equation for WACC is:
WACC = (E/V)RE + (D/V)RD(1 – tC)
The company has a debt-equity ratio of 1.5, which implies the weight of debt is 1.5/2.5, and the
weight of equity is 1/2.5, so
WACC = .12 = (1/2.5)RE + (1.5/2.5)(.12)(1 – .35)
RE = .1830 or 18.30%
b.
To find the unlevered cost of equity we need to use M&M Proposition II with taxes, so:
RE = RU + (RU – RD)(D/E)(1 – tC)
.1830 = RU + (RU – .12)(1.5)(1 – .35)
RU = .1519 or 15.19%
c.
To find the cost of equity under different capital structures, we can again use the WACC
equation. With a debt-equity ratio of 2, the cost of equity is:
.12 = (1/3)RE + (2/3)(.12)(1 – .35)
RE = .2040 or 20.40%
With a debt-equity ratio of 1.0, the cost of equity is:
.12 = (1/2)RE + (1/2)(.12)(1 – .35)
RE = .1620 or 16.20%
And with a debt-equity ratio of 0, the cost of equity is:
.12 = (1)RE + (0)(.12)(1 – .35)
RE = WACC = .12 or 12%
CHAPTER 17 B-269
13. a.
For an all-equity financed company:
WACC = RU = RE = .14 or 14%
b.
To find the cost of equity for the company with leverage we need to use M&M Proposition II
with taxes, so:
RE = RU + (RU – RD)(D/E)(1 – tC)
RE = .14 + (.14 – .10)(.25/.75)( 1 – .35)
RE = .1487 or 14.87%
c.
Using M&M Proposition II with taxes again, we get:
RE = RU + (RU – RD)(D/E)(1 – tC)
RE = .14 + (.14 – .10)(.50/.50)(1 – .35)
RE = .1660 or 16.60%
d.
The WACC with 25 percent debt is:
WACC = (E/V)RE + (D/V)RD(1 – tC)
WACC = .75(.1487) + .25(.10)(1 – .35)
WACC = .1278 or 12.78%
And the WACC with 50 percent debt is:
WACC = (E/V)RE + (D/V)RD(1 – tC)
WACC = .50(.1660) + .50(.10)(1 – .35)
WACC = .1155 or 11.55%
14. a.
The value of the unlevered firm is:
V = EBIT(1 – tC)/RU
V = INR4,000,000(1 – .35)/.20
V = INR13,000,000
b.
The value of the levered firm is:
V = V U + t CD
V = INR13,000,000 + .35(INR2,500,000)
V = INR13,875,000
B-270 SOLUTIONS
15. We can find the cost of equity using M&M Proposition II with taxes. Doing so, we find:
RE = RU + (RU – RD)(D/E)(1 – t)
RE = .20 + (.20 – .11)(INR2,500,000/INR11,375,000)(1 – .35)
RE = .2129 or 21.29%
Using this cost of equity, the WACC for the firm after recapitalization is:
WACC = (E/V)RE + (D/V)RD(1 – tC)
WACC = .2129(INR11,375,000/INR13,875,000) + .11(1 – .35)(INR2,500,000/INR13,875,000)
WACC = .1874 or 18.74%
When there are corporate taxes, the overall cost of capital for the firm declines the more highly
leveraged is the firm’s capital structure. This is M&M Proposition I with taxes.
Intermediate
16. To find the value of the levered firm we first need to find the value of an unlevered firm. So, the value
of the unlevered firm is:
VU = EBIT(1 – tC)/RU
VU = (BRL75,000)(1 – .35)/.14
VU = BRL348,314.29
Now we can find the value of the levered firm as:
V L = V U + t CD
VL = BRL348,314.29 + .35(BRL150,000)
VL = BRL400,714.29
Applying M&M Proposition I with taxes, the firm has increased its value by issuing debt. As long as
M&M Proposition I holds, that is, there are no bankruptcy costs and so forth, then the company
should continue to increase its debt/equity ratio to maximize the value of the firm.
17. With no debt, we are finding the value of an unlevered firm, so:
V = EBIT(1 – tC)/RU
V = €10,000(1 – .35)/.17
V = €38,235.29
With debt, we simply need to use the equation for the value of a levered firm. With 50 percent debt,
one-half of the firm value is debt, so the value of the levered firm is:
V = V U + t CD
V = €38,235.29 + .35(€38,235.29/2)
V = €44,926.47
CHAPTER 17 B-271
And with 100 percent debt, the value of the firm is:
V = V U + t CD
V = €38,235.29 + .35(€38,235.29)
V = €51,617.65
Challenge
18. M&M Proposition II states:
RE = RA + (RA – RD)(D/E)(1 – tC)
And the equation for WACC is:
WACC = (E/V)RE + (D/V)RD(1 – tC)
Substituting the M&M Proposition II equation into the equation for WACC, we get:
WACC = (E/V)[RA + (RA – RD)(D/E)(1 – tC)] + (D/V)RD(1 – tC)
Rearranging and reducing the equation, we get:
WACC = RA[(E/V) + (E/V)(D/E)(1 – tC)] + RD(1 – tC)[(D/V) – (E/V)(D/E)]
WACC = RA[(E/V) + (D/V)(1 – tC)]
WACC = RA[{(E+D)/V} – tC(D/V)]
WACC = RA[1 – tC(D/V)]
19. The return on equity is net income divided by equity. Net income can be expressed as:
NI = (EBIT – RDD)(1 – tC)
So, ROE is:
RE = (EBIT – RDD)(1 – tC)/E
Now we can rearrange and substitute as follows to arrive at M&M Proposition II with taxes:
RE = [EBIT(1 – tC)/E] – [RD(D/E)(1 – tC)]
RE = RAVU/E – [RD(D/E)(1 – tC)]
RE = RA(VL – tCD)/E – [RD(D/E)(1 – tC)]
RE = RA(E + D – tCD)/E – [RD(D/E)(1 – tC)]
RE = RA + (RA – RD)(D/E)(1 – tC)
B-272 SOLUTIONS
20. M&M Proposition II, with no taxes is:
RE = RA + (RA – Rf)(D/E)
Note that we use the risk-free rate as the return on debt. This is an important assumption of M&M
Proposition II. The CAPM to calculate the cost of equity is expressed as:
RE = E(RM – Rf) + Rf
We can rewrite the CAPM to express the return on an unlevered company as:
RA =  A(RM – Rf) + Rf
We can now substitute the CAPM for an unlevered company into M&M Proposition II. Doing so
and rearranging the terms we get:
RE =  A(RM – Rf) + Rf + [A(RM – Rf) + Rf – Rf](D/E)
RE =  A(RM – Rf) + Rf + [A(RM – Rf)](D/E)
RE = (1 + D/E) A(RM – Rf) + Rf
Now we set this equation equal to the CAPM equation to calculate the cost of equity and reduce:
E(RM – Rf) + Rf = (1 + D/E) A(RM – Rf) + Rf
E(RM – Rf) = (1 + D/E)A(RM – Rf)
E =  A(1 + D/E)
21. Using the equation we derived in Problem 20:
E =  A(1 + D/E)
The equity beta for the respective asset betas is:
Debt-equity ratio
0
1
5
20
Equity beta
1(1 + 0) = 1
1(1 + 1) = 2
1(1 + 5) = 6
1(1 + 20) = 21
The equity risk to the shareholder is composed of both business and financial risk. Even if the assets
of the firm are not very risky, the risk to the shareholder can still be large if the financial leverage is
high. These higher levels of risk will be reflected in the shareholder’s required rate of return RE,
which will increase with higher debt/equity ratios.